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The view from Earth
Constellations
Definition: group of stars within limited angular distance of each other that suggest a
familiar shape
- there are 88 constellations
-constellations completely tile the sky and do not overlap
 every star belongs to one, and only one, constellation
- NOTE: most stars in a constellation are not physically associated with each other
-can have very different linear distances from Earth
 stars in a constellation would be separated by very large angular distances if
viewed from another star
Different constellations are in the night sky at different times of year
- due to Earth’s revolution around Sun (see “Celestial sphere” section)
Star names:
Historic names:
- stars that are bright enough to be readily visible to the naked eye (a tiny fraction of all
stars) have historic names inherited from ancient civilizations (often Arabic)
- still in common use
- egs. Sirius (the brightest star in the sky), Polaris (the “pole star”), Vega, Betelgeus,
Deneb, Antares, Procyon, Altair, Rigel, Spica, Fomalhaut, Capella, Arcturus,
Aldebaran, Castor, Pollux, Achernar, etc.
- these names are not systematic
- they do not provide a system for assigning a name to each and every star
- the names do not convey information about the star
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A system for naming stars: the Bayer system
-
any star can be uniquely identified with a two part name:
-
note: most stars with historical names are among the brightest in their
constellation. Therefore, they have modern names beginning with one of
the first few letters of the Greek alphabet (α, β, γ, δ, or ε).
- second part is possessive form of name of constellation in which star is
located
- Greek possessive form: egs. a star in Pereus has the name Persei, a star
in Gemini has the name Geminorum, etc.)
- first part is a Greek letter or an Arabic numeral based on star’s relative
brightness (as seen from Earth) in its constellation
- alpha (α): brightest, beta (β): second brightest, gamma (γ): third
brightest, delta (δ): fourth brightest, epsilon (ε): fifth brightest, etc.
 24 letters of Greek alphabet assigned to 24 brightest stars in
constellation
- starting with 25th brightest star, first name is an Arabic numeral, starting
with 1 and increasing with decreasing brightness
eg. α Orionis (Betelgeus): brightest star in constellation Orion
α Lyra (Vega): brightest star in constellation Lyra
β Geminorum (Pollux): second brightest star in constellation Gemini
61 Cygni (a solar analog): relatively faint star in constellation Cygnus
Diurnal motion:
Diurnal is Latin for “daily”
Definition of diurnal motion: daily westward motion across the sky followed by all
celestial objects, including constellations
- Motion is cyclic with a period of ~24 hours
- due to Earth’s rotation:
 Earth rotates eastward with a rotation period of ~24 hours
- angular rate of diurnal motion = 360o/24hrs = 15o/1hr
 diurnal motion carries celestial objects westward at a rate of 15o/hr
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The celestial sphere (CS):
Definition: A simplified model of the Universe useful for describing positions and
motions of celestial objects, as viewed from Earth
Simplifying assumptions:
1) The Earth is located at the center of the Universe
2) All celestial objects (Moon, Sun, planets, stars, etc.) are at the same linear distance
from Earth
ie. as if all celestial objects were affixed on inside of a giant celestial sphere that is
centered on Earth
3) That Earth does not rotate
 diurnal motion due to westward rotation of CS
Special imaginary points and lines on celestial sphere:
Helpful geometric terminology:
-
Great circle: a line on the surface of a sphere that bisects the sphere
- a great circle is the largest circle that can be described on the surface of a
sphere
- there can be many distinct great circles on the surface of a sphere, all
inclined (tilted) to one another by some angle
-
Small circle:
- any circle on the surface of a sphere that is not a great circle
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North celestial pole (NCP): point on CS directly above Earth’s north pole
South celestial pole (SCP): point on CS directly above Earth’s south pole
 poles are the pivot points for the Celestial Sphere’s diurnal rotation
Note: by pure luck there happens to be a bright star very close to the NCP; the star
Polaris (the “pole star”). There is no bright star close to the SCP, ie. there is no
southern pole star
Celestial equator (CE): a great circle on CS half-way between the NCP and SCP
 the CE lies directly above Earth’s equator
Note: The CE bisects the CS, ie. divides the CS into two equal hemispheres
Great circle: any line on the surface of a sphere that bisects it
 the CE is a great circle
North celestial hemisphere: the half of the CS that is north of the CE
South celestial hemisphere: the half of the CS that is south of the CE
More precise description of diurnal motion:
Celestial objects move across sky along small circles that are parallel to the CE and that
are centered on the NCP (or SCP in southern hemisphere), taking ~24 hours to complete
their circular path
- diurnal path: the small circle that an object travels around on the CS once each day
Imaginary points and lines on CS defined with respect to the Observer:
Zenith: point on CS directly above observer
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Zenith distance, z: angular distance with respect to center of Earth of celestial object
from Zenith
Horizon: great circle on CS on which every point has a zenith distance of 90o
- significance: can only see objects on CS that are above horizon
Altitude, a: angular distance with respect to center of Earth of a point from horizon
- eg. the zenith has a = 90o
- Note: altitude and zeith distance are complementary angles (ie. for any object: a +
z = 90o)
Azimuth, φ: angular distance with respect to center of Earth clockwise along horizon
- φ increases by 360o around entire horizon
Meridian: line on CS passing through zenith and NCP (or SCP in southern hemisphere)
 ie. meridian runs in north-south direction across sky
- significance: meridian bisects sky into eastern and western halves
North point (N): point on horizon through which Meridian passes (in northern
hemisphere)
- by definition N has azimuth, φ = 0o
- Earth’s rotation defines the cardinal directions:
- eg. East (E) is a point on the horizon that has φ = 90o
- - ie. a point 90o clockwise around horizon from the N point
 By definition: Earth rotates eastward
egs. South (S) has φ = 180o, West (W) has φ = 270o
-
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Note on direction of Earth’s rotation:
Earth rotates counter-clockwise (CCW) when viewed from above the North pole
looking down onto plane of Earth’s equator
 by definition any circular motion in the plane of Earth’s equator that is CCW as
seen from above the North pole looking down is said to be Eastward motion
AND
 any object that moves Eastward across the CS is revolving CCW with respect to
Earth as seen from above Earth’s North pole looking down onto the plane of its
orbit
Transit:
A celestial object is transiting when it crosses the Observer’s meridian
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- time of transit of an object is relative
 depends on Observer’s longitude
- significance: object has maximum altitude when transiting
- note: all celestial objects transit once a day due to diurnal motion
Related quantities:
Latitude: Altitude of NCP  ie. angular distance from N point to NCP.
- depends on location of observer
Eg 1. Observer at the equator:
The NCP is on the observer’s Horizon
 N point is at the NCP
 altitude of NCP = 0o
 latitude = 0o
Eg 2. Observer at the north pole:
The NCP is at the observer’s Zenith
 N point is on the observer’s Horizon (always true by definition!)
 altitude of NCP = 90o
 latitude = 90o
Co-latitude: Zenith distance, z, of NCP
- note: latitude and co-latitude are complementary angles
- like latitude, depends on location of Observer
Circumpolar stars: stars that are above the observer’s horizon 24 hours per day
- stars for which the diurnal path is entirely above the observer’s horizon
- circumpolar stars never rise and set, they are always in the sky (but they cannot be
seen during the day because the sky is too bright)
- Which stars are circumpolar depends on observer’s latitude:
 If angular distance of star from NCP < observer’s latitude  star is circumpolar
- eg. at N. pole (latitude = 90o) all stars in northern celestial hemisphere are
circumpolar
- eg. at equator (latitude = 0o) no stars are circumpolar
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The Sun: Seasons and the Ecliptic
Seasons
- follow annual cycle
- opposite in Northern and Southern hemispheres
What causes the seasons? The Ecliptic:
Ecliptic: The Sun’s annual path on the Celestial Sphere (CS)
 ie. the Sun’s position on the CS changes throughout the year
- the ecliptic is a great circle (ie. it bisects the CS)
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- serves as an important reference line on CS, like celestial equator
Earth is undergoing two different circular motions simultaneously: Rotation and
Revolution
- Rotation: circular motion around an internal axis
- Earth: rotation around axis that joins Earth’s North and South poles
Rotational Period (PRot) ~ 24 hours
- cause of diurnal motion, including that of the Sun
- Revolution: circular motion around an external axis
- Earth: revolution around axis that passes through the center of the Sun
Revolutionary Period (PRev) ~ 365 days
- cause of the Sun’s annual motion around the ecliptic
The Earth revolves around the Sun with a period of one year
 our line of sight to the Sun rotates by 360o each year
 as seen from Earth, the Sun travels 360o around the Celestial Sphere each year
 the Ecliptic is the path on the CS that the Sun follows
Earth does not revolve around other stars
AND other stars very far away compared to Sun
 position of other stars on CS almost completely fixed
 Sun’s position with respect to all other stars changes throughout year
 ecliptic is Sun’s annual path on the CS with respect to the stars
Zodiac: Band on CS centered on ecliptic containing the constellations that the Sun passes
in front of throughout year
- twelve constellations in Zodiac: Sagittarius, Capricornus, Aquarius, Pisces, Aries,
Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpius
Rate of change of Sun’s angular position on CS (ie. Sun’s angular velocity):
Rate = 360o / (Earth’s revolutionary period)
= 360o / 365 days
= 0.986o/day
 ie. Sun’s angular position on CS changes by ~ 1o/day
Direction of Sun’s motion along ecliptic:
- Earth revolves around Sun in same direction that Earth rotates on its axis: Eastward
(ie. Earth’s orbital motion around Sun is CCW)
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 line of sight from Earth to Sun rotates eastward
 Sun’s position on CS moves Eastward
 ie. Sun travels eastward along ecliptic by ~ 1o/day
-note: rate = 24h /365d = (24h × 60m/hour)/365d = 1440m/365d = 4m/day
 in time on daily clock: Sun rises 4m later with respect to stars each day
Note: Sun is undergoing two motions on CS simultaneously:
1) Diurnal motion:
- westward motion around CS every 24 hours on a diurnal path
- due to Earth’s rotation around its own axis
2) Annual motion around the ecliptic:
- eastward motion around CS every 365 days along the ecliptic
- due to Earth’s revolution around Sun
Obliquity of the Ecliptic:
Plane of the ecliptic: the plane defined by Earth’s orbit around the Sun
- any revolving body moves along a circular orbit, and any circle lies in a plane
 ie. revolution defines an orbital plane
- the ecliptic lies in the plane of Earth’s orbit, by definition of the ecliptic
Equatorial plane: the plane defined by Earth’s rotation
-any spinning body rotates in a plane that is perpendicular to its rotation axis
 rotation also defines a plane
- the Celestial Equator (CE) lies in the Equatorial plane
Inclination of Earth’s rotation axis: Earth’s rotation axis is not perpendicular to the
plane of its orbit: it is inclined (ie. tilted) from the perpendicular by 23o.5
 ie. inclination of Earth’s rotational axis, i, is 23o.5
 The Ecliptic is inclined by 23o.5 with respect to the Celestial Equator
 the obliquity (ie. tilt with respect to the CE) of the ecliptic is 23o.5
 The line of latitude directly under the Sun’s diurnal path changes throughout year
from –23o.5 to +23o.5 and
back
- ie. the ecliptic is NOT co-incident with the CE AND is NOT parallel to the CE
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Equinoxes and Solstices:
Ecliptic and Celestial Equator (CE): two great circles on Celestial Sphere (CS) that are
inclined to one another (by 23o.5)
 the Ecliptic and the CE cross at two points on CS
Equinox: either of two points on the CS where the Ecliptic and the CE cross
 two equinoxes are on opposite sides on the CS from each other (ie. the angular
distance between them is 180o)
 at Equinox Sun’s declination, δ = 0o
Vernal Equinox (): point on CS where Sun crosses the CE going from the South
celestial hemisphere to the North celestial hemisphere
- also known as the Spring Equinox
- located near the constellation Aries  represented with the symbol for Aries: 
-  is fixed with respect to stars  moves westward with rotation of Celestial Sphere
 co-ordinate system rotates with diurnal motion
Autumnal Equinox: point on CS where Sun crosses the CE going from the North
celestial hemisphere to the South celestial hemisphere
Solstice: either of two points on the CS where the angular distance of the Sun from the
CE is largest (ie. where it is 23o.5)
Summer solstice: point on CS where Sun is 23o.5 North of CE
Winter solstice: point on CS where Sun is 23o.5 South of CE
Seasons:
The Equinoxes and Solstices are fixed points on the ecliptic
 the Sun reaches each Equinox and Solstice on the same calendar date every year
 the Equinoxes and solstices are also times of year as well as points on the CS
Point on Ecliptic
Vernal Equinox
Summer Solstice
Autumnal Equinox
Winter Solstice
Date Sun is at point
March 21
June 21
Sept 21
Dec 21
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Climate depends on Sun’s position on CS:
The diurnal path of a celestial object lies directly above the line of latitude equal to its
declination ()
 Sun passes directly over the line of latitude equal to its  on a given date
Near Summer Solstice: Sun’s diurnal path is North of CE
 In Northern hemisphere:
- more than half of Sun’s diurnal path is above horizon
 Sun is above horizon for more than 12 hours per day
 Sun zenith distance is small around mid-day
 Sunlight is more direct near mid-day (ie. we are being illuminated from almost
directly overhead)
 Northern hemisphere experiences summer climate
 In Southern hemisphere:
- less than half of Sun’s diurnal path is above horizon
 Sun is above horizon for less than 12 hours per day
 Sun zenith distance is large around noon
 Sunlight is less direct near mid-day
 Southern hemisphere experiences winter climate
Significance of Equinoxes: At Equinox Sun’s diurnal path is above equator
 At equator, Sun is above horizon for exactly 12 hours
 day and night equal in length
 “Equinox” is Latin for “equal night”
Near Winter Solstice: Sun’s diurnal path is South of CE
- conditions described above are reversed between Northern and Southern hemispheres
 Northern hemisphere experiences winter climate
Southern hemisphere experiences summer climate
CAUTION: the seasons are opposite in the Northern and Southern hemispheres
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- the names of the Summer and Winter solstice are only appropriate for the Northern
hemisphere
NOTE: the seasons are NOT due to Earth’s distance from the Sun changing throughout
year
- Earth’s orbit almost perfectly circular with Sun at center
 Earth’s distance to Sun stays almost the same throughout year
(In fact, the Earth is closest to the Sun on January 4!)
Location of Sunrise & Sunset:
Azimuths at which Sun rises and sets changes throughout year
- on June 21: Sun’s diurnal path is 23o.5 North of CE
 Sunrise is 23o.5 North of East-point; ie. East by North-east
 Sunset is 23o.5 North of West-point; ie. West by North-west
- on Dec 21: Sun’s diurnal path is 23o.5 South of CE
 Sunrise is 23o.5 South of East-point; ie. East by South-east
 Sunset is 23o.5 South of West-point; ie. West by South-west
- on Mar 21 and Sep 21: Sun’s diurnal path is coincident with the CE
 Sunrise is at the East-point
 Sunset is at the West-point
Tropics & Arctic Circles:
The diurnal path of a celestial object lies directly above the line of latitude equal to its
declination ()
 once a day a celestial object passes through the zenith of any observer located on the
line of latitude equal to its 
Tropics: Either of two lines of latitude equal to maximum and minimum declination ()
reached by Sun during year
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-ie. either of two lines of latitude equal to + or – Earth’s orbital inclination, i, ie. +/23o.5
- Tropic of Cancer: latitude = +23o.5 (23o.5 N)
- Sun at Zenith at noon at Summer Solstice
- Tropic of Capricorn: latitude = -23o.5 (23o.5 S)
- Sun at Zenith at noon at Winter Solstice
-
-Tropical Zone (or “the tropics”): refers to range of latitudes between Tropic of
Cancer and Tropic of Capricorn (ie. from +23o.5 to –23o.5)
 within the Tropical Zone the Sun is at Zenith at noon twice per year
- zenith distance, z of Sun always < 47o  little seasonal variation in climate
 outside the Tropical Zone the Sun is never at the zenith
- the Equator is at center of Tropical Zone (latitude = 0o)
Arctic Circles: Either of two lines of latitude equal to + or – (90o – Earth’s orbital
inclination)
- ie. equal to +/-(90o – 23o.5) = +/-66o.5
- “Antarctic” circle: the arctic circle at –66o.5
-
Arctic Zones: range of latitudes from +66o.5 to +90o (Arctic) AND from –66o.5 to
–90o (Antarctic)
- poles at centers of Arctic zones
- Significance:
At Arctic circle:
- when Sun’s  = +23.5o (Jun 21), zenith distance of Sun  90o for entire day
 ie. Sun is circumpolar
 Sun never sets
- when Sun’s  = -23.5o (Dec 21), zenith distance of Sun  90o for entire day
 Sun never rises
At Antarctic circle:
- when Sun’s  = -23.5o (Dec 21), zenith distance of Sun  90o for entire day
 Sun never rises
- when Sun’s  = +23.5o (Jun 21), zenith distance of Sun  90o for entire day
 Sun never sets
Temperate zones: bands of latitude between tropical zone and arctic circle
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 latitude ranges: +23.5o to +66.5o and -23.5o to -66.5o
Precession (precession of the equinoxes):
- slow “wobble” of Earth’s rotation axis
Earth: Earth precesses because Moon’s gravity tries to rotate direction of Earth’s
rotation axis
 Moon’s gravity tries to pull Earth “upright”
ie. tries to rotate Earth’s rotational axis around an axis perpendicular to the
rotation axis
 Earth’s rotation axis precesses slowly around perpendicular to plane of it’s
orbit
 As rotation axis gyrates, plane of Earth’s Equator wobbles
 ie. NCP is NOT always at Polaris!
Precession period = 26,000 years  gyration of rotation axis very slow
Consequences of precession: precession of the equinoxes:
As rotation axis gyrates
- positions of North and South Celestial Poles (NCP & SCP) on Celestial Sphere
(CS) change
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- position of Celestial Equator (CE) on CS changes
 declination, δ, of stars change with time
- BUT: position of Ecliptic on CS DOES NOT change
 ecliptic defined by plane of Earth’s orbit, NOT by orientation of Earth’s
equator
 CE wobbles while Ecliptic remains fixed
 position of Equinoxes on CS slowly moves westward around ecliptic with
period of 26,000 years
Celestial time-keeping
-
Astronomical cycles ARE the basis of civil clocks and calendars!
Daily clock:
- determined by Sun’s diurnal motion
Local apparent noon: instant when Sun is transiting (ie. is on the Observer’s meridian
– see earlier notes)
- depends on longitude of observer
Apparent solar day: time interval between successive transits by the Sun
- length of time for Earth to rotate ~361o, not 360o
- apparent solar day is what we actually experience
Time Zones:
- When noon occurs depends on observer’s longitude
- Diurnal motion of Sun is 360o/(solar day) = 15o/hour
 24 time zones of angular width = 15o centered on lines of longitude 15o apart
Co-ordinated Universal Time (UTC): mean solar time at Greenwich, England
(longitude = 0o)
- also called Universal Time (UT)
- useful for situations where people in different time-zones need to refer to a common
clock
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Annual Calendar:
- determined by Sun’s motion along ecliptic
Sidereal year: interval between successive passages of Sun through same place on
Celestial Sphere (CS) with respect to the stars
= Period of Earth’s orbit around Sun (Porb)
= 365.2564 mean solar days
 sidereal year ~ 365.25 mean solar days
Problem: sidereal year is NOT equal to a whole number of mean solar days
 there is an extra ~¼ (~0.25) days beyond 365 days
 in an exact sidereal calendar the New Year would start ~¼ day (~6 hours) later in
the Mean Solar Day each year
Julian Calendar:
- implemented by Julius Ceasar (hence “Julian”)
 used until 16th Century
- designed to give an average year of 365.25 days while keeping a whole number of days
in any given year
- gives Julian year: an average year exactly equal to 365.25 days
 Julian year slightly shorter than sidereal year by 0.0064 days
- Rule for Julian calendar:
- any year evenly divisible by four is a leap year and has 366 days, by adding Feb 29
- all other years have 365 days
 gives four year cycle:
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- first three years have 365 days
- fourth year has 366 days
 average year over cycle has 365.25 days  close to sidereal year
Tropical year: interval between successive passages of Sun through same place on CS
with respect to the Vernal Equinox ()
= 365.2422 mean solar days
  is precessing westward around the ecliptic (see section on Precession above)
 time for Sun to return to same place with respect to  is less than time for Sun to return
to same place with respect to stars
 tropical year is shorter than sidereal year by 20m 24s
Significance of tropical year: tropical year is length of complete cycle of four seasons
 useful for agriculture, seasonal religious rituals
Problem with Julian calendar:
- Julian year is longer than tropical year by 11m14s
 calendar dates of beginning of seasons slowly changing
 by 16th Century Sun was passing through γ on Mar 11
Gregorian calendar: improvement to Julian calendar
- implemented by Pope Gregory VIII in 16th C. (hence “Gregorian”)
- gives Gregorian year: - almost exactly equal to tropical year
- any year has whole number of days (like Julian calendar)
- Rule for Gregorian calendar:
- all years divisible by four have are leap years and have 366 days except Century
years NOT divisible by 400
- all other years have 365 days
- eg. In Julian calendar 1900 and 2000 are both leap years
In Gregorian calendar 2000 is a leap year, but 1900 is NOT
- gives 400 year cycle:
 average year over 400 year cycle almost exactly equal to tropical year
 Gregorian calendar almost exactly synchronous with cycle of seasons
 Gregorian calendar is still in use today, is modern civil calendar
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The Moon
-
plane of Moon’s orbit around Earth is inclined by 5o to plane of Earth’s orbit around
Sun
 Moon is always within 5o of ecliptic
 Moon is a zodiacal object, ie. it moves through the band of 12 zodiacal
constellation that the ecliptic passes through
-
Orbital period (Porb) ~ 4 weeks
 Moon takes ~4 weeks to move 360o around Celestial Sphere
 Rate of Moon’s motion on CS: 360o/28days = 12.86o/day
-
Moon revolves around Earth Eastward (ie. CCW as seen from above North pole
looking down)
 Moon moves Eastward along Celestial Sphere (like Sun)
 Moon’s motion across CS much faster than that of Sun
 angular distance from Sun to Moon, measured eastward, increases from 0o to
360o every ~4 weeks
-
-
Lunar Phases
Moon reflects sunlight (like a mirror)
 Moonlight is reflected sunlight
Lunar phase: portion of the Moon that is illuminated by the Sun, as seen from Earth
-
lunar phase depends on angular distance between Moon and Sun
 lunar phases are cyclic with period ~Porb (~4 weeks)
Terminology to describe lunar phases:
- Waxing (“increasing in strength”): illuminated portion of Moon is increasing from
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one night to the next
- occurs when angular distance from Sun to Moon measured eastward is greater
than 0o and less than 180o
- Western side of Moon is illuminated
- Waning (“decreasing in strength”): illuminated portion of Moon is decreasing from
one night to the next
- occurs when angular distance from Sun to Moon measured eastward is greater
than 180o and less than 360o
- Eastern side of Moon is illuminated
- New:
- Full:
Moon not illuminated as seen from Earth, is invisible
 Moon back-lit by Sun
occurs when angular distance between Sun and Moon is ~0o
shape of Moon when it is completely illuminated; a full circular disk
occurs when angular distance between Sun and Moon is ~180o
- Crescent: shape of Moon when less than half of it is illuminated; crescent shaped
occurs when absolute angular distance between Sun and Moon is less than
90o
- Gibbous: shape of Moon when more than half of it is illuminated; lens shaped
occurs when absolute angular distance between Sun and Moon is more than
90o
- Quarter: shape of Moon when exactly half of it is illuminated; a half circular disk
occurs when absolute angular distance between Sun and Moon is ~90o, hence
“quarter”
-First quarter (Q1): quarter Moon when Moon is waxing
occurs when angular distance from Sun to Moon measured
eastward is ~90o
western half of Moon illuminated
-Third quarter (Q3): quarter Moon when Moon is waning
occurs when angular distance from Sun to Moon measured
eastward is ~270o
eastern half of Moon illuminated
Cycle of lunar phases:
Phase
Ang. Dist. Sun-Moon
Eastward
Time since
New Moon
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New
Waxing crescent
First Quarter
Waxing gibbous
Full
Waning gibbous
Third Quarter
Waning crescent
New
0o
45o
90o
135o
180o
225o
270o
305o
360o
0 weeks
0.5 weeks
1 week
1.5 weeks
2 weeks
2.5 weeks
3 weeks
3.5 weeks
4 weeks
Time of Moonrise and Moonset:
-
angular distance from Sun eastward to Moon increases by 360o over ~4 weeks
 the local solar time at Moonrise and Moonset increases by 24h over ~4 weeks
-eg. At New Moon:
- angular distance from Sun eastward to Moon is ~0o
 Moon rises when Sun rises, and sets when Sun sets
(makes sense: Sun and Moon at same place on Celestial Sphere!)
-eg. At Full Moon:
- angular distance from Sun eastward to Moon is ~180o
 Moon rises when Sun sets, and sets when Sun rises
(makes sense: Sun and Moon at opposite sides of Celestial Sphere!)
The Moon and the Calendar: the Month
- related to Moon’s cyclic motion around the CS
Sidereal Month (Sidereal Period, Psidereal): Time for Moon to return to same place on
Celestial Sphere (CS) with respect to Stars
-
Psidereal = 27.3 solar days
Psidereal = Moon’s orbital period (ie. Psidereal = Porb)
= time for Moon to travel 360o around CS
Recall: “Sidereal” means “having to do with stars”
Synodic Month (Synodic Period, Psynod): Time for Moon to return to same place on
Celestial Sphere (CS) with respect to Sun
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-
“Synod”: Hebrew for Sun
Psynod = 29.5 mean solar days (ie. Psynod > Psidereal)
-
Significance: Synodic month is length of cycle of lunar phases
Synodic month is almost equal to calendar month (average calendar
month ~30.5 days)
 same lunar phases do not occur on same date each month
Sun & Moon both move Eastward on CS
- Sun moves Eastward by ~ 1o/day
 Moon must travel 360o + 27o.3 = 387o.3 around CS between subsequent coincidences with Sun
 Psynod > Psidereal
Rotation of the Moon
-
-
Moon undergoing two circular motions simultaneously: Revolution & Rotation
(like Earth)
- Moon revolves around axis through center of Earth oriented perpendicular to
plane of its orbit
- due to its orbital motion
- Prev = Porb = Psidereal = 27.3 solar days
- Moon rotates around axis through center of Moon oriented perpendicular to
plane of its orbit
- ie. Moon is spinning around its own axis, like Earth
- Moon rotates Eastward (ie. CCW as seen from above North pole looking
down)
 same as direction of revolution (ie. a “top-spin”)
- Prot = 27.3 solar days = Porb
Moon’s Synchronous rotation:
-For Moon, Prot = Porb (For Earth: Prot (24 hours) << Porb (365 days))
 Moon rotates with exactly the same period as it revolves
 Moon’s rotation is synchronized to its orbit (it rotates synchronously)
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Also referred to as “spin-orbit coupling”, “spin-orbit locking”, “tidal
coupling”, “tidal locking”
-
Consequences of synchronous rotation:
- Moon is a one-face body
 Moon always keeps the same side facing toward Earth as it revolves
 From Earth we only ever see the “near side”
- On Moon: - length of solar day = Psynodic = 29.5 Earth solar days
- Earth always at same position on lunar sky!
Lunar and Solar Eclipses
Earth & Moon both cast shadows
-
Sun only light source  shadows point directly away from direction to Sun
Sun very far away  shadows are long and narrow
Lunar eclipse: occurs when Earth’s shadow falls on Moon
-
Moon is eclipsed by Earth
Earth must be between Sun and Moon
 angular distance between Sun and Moon is 180o
 lunar phase is Full
Solar eclipse: occurs when Moon’s shadow falls on Earth
-
Sun is eclipsed by Moon
Moon must be between Sun and Earth
 angular distance between Sun and Moon is 0o
 lunar phase is New
Rarity of eclipses:
Region of complete shadow very narrow
 need exact alignment of Earth-Moon-Sun for eclipse
AND: plane of Moon’s orbit inclined by 5o to plane of Earth’s orbit (plane of ecliptic)
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 exact three-body alignment very rare
 most occurences of New and Full Moon are NOT accompanied by eclipse
Parts of a shadow:
- Umbra: region of complete shadow
- lies near center of shadow
- for observer in umbra, eclipsing object completely blocks eclipsed object
- Penumbra: region of partial shadow
- lies near edge of shadow
- for observer in penumbra, eclipsing object partially blocks eclipsed object
- Umbra and penumbra geometrically defined by grazing incidence rays from light
source to eclipsing object (see diagram)
Lunar eclipse:
Total eclipse: Moon entirely in umbra of Earth’s shadow
Partial eclipse: Moon partially in umbra of Earth’s shadow
Note: If Moon in penumbra of Earth’s shadow
 no noticeable dimming of Moon
 not considered to be an eclipse
Totality: condition of total eclipse
-
duration of totality:
- depends on Moon’s path through shadow
- maximum duration ~1h42m
appearance of totality:
- Moon dims and becomes red, but does not disappear
 red light from Sun refracts through Earth’s atmosphere and reaches Moon
Accessibility:
Lunar phase is Full  eclipse visible to everyone on Earth’s night-side
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Solar eclipse:
Accessibility:
-
Moon and Sun almost exactly same angular diameter (0.o5) (as seen from Earth)
 Moon just barely large enough on Celestial Sphere to block out Sun
 Umbra of Moon’s shadow just barely reaches Earth’s surface
 only small area of Earth’s surface in umbra during eclipse
Observer in umbra: total solar eclipse
Observer in penumbra: partial solar eclipse
Observer outside of shadow: no eclipse
 ie. type of eclipse (or whether there’s an eclipse at all) depends on observer’s
location on surface
Eclipse path: path of umbra as it moves across Earth’s surface during eclipse
- umbra moves across surface with speed ~1700 km/h
 maximum duration of totality: ~7.5 minutes
Annular eclipse:
-
Moon’s orbit not perfectly circular
 Moon-Earth distance varies
AND:
Earth’s orbit not perfectly circular
 Earth-Sun distance varies
 angular diameter of Moon and Sun vary slightly
When Moon’s angular diameter < Sun’s angular diameter
 Moon’s umbra does not reach Earth’s surface
 Moon cannot eclipse entire Sun
 observer near center of shadow sees an annulus (ie. a ring) of Sun around
Moon (hence “annular” eclipe)
 During an annular eclipse there is NO totality for any observer
Appearance of eclipse:
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-
Photosphere: part of Sun that appears as opaque yellow disk
- the photosphere is by far the brightest part of Sun
 is only part of Sun we can normally see
 during totality the photosphere is eclipsed by the Moon
During totality can see solar chromosphere and corona:
- parts of Sun that are normally invisible due to the glare of the photosphere
Chromosphere: narrow ring of faint pink glowing gas surrounding photosphere
- “Chromos”: Latin for color
Corona: extended halo of very faint glowing gas surrounding chromosphere
- extends out to 12  radius of photosphere
- complex structure